Theresa May and Brandon Lewis, the Conservative Party chairman, and Scottish Conservative leader Ruth Davidson have all called on Mr Johnson to apologise for the comments.

He has so far refused to do so, with allies insisting the criticism of his comments was "ridiculous".

The probe will investigate whether Mr Johnson breached the party's code of conduct, which says members must "lead by example to encourage and foster respect and tolerance".

It will initially focus on collecting evidence and statements to determine whether the inquiry should proceed. Mr Johnson will be given the opportunity to provide a statement outlining "any evidence or details that will help establish their position".

If there is deemed to be enough evidence of a breach of rules, a disciplinary panel consisting of at least three people will be appointed by Mr Lewis. Graham Brady, the chair of the 1922 committee of Tory MPs, will select one member.

The panel will determine whether Mr Johnson broke any rules and pass its conclusions to Ms May and the Conservative Party board, who will decide what punishment, if any, he should face.

Two Tory peers are among those who have called for disciplinary action to be taken against Mr Johnson.

Lord Sheikh, the founder of the Conservative Muslim Forum, said he had written to Mr Lewis calling for "severe action" and suggesting the whip be removed from the former foreign secretary.

Baroness Warsi, a former co-chair of the party, called Mr Johnson's comments "reprehensible" and said there should be "real action" and "consequences" if he refuses to apologise.

As well as the complaints made to the Conservatives, Mr Johnson has also been reported to the police and to the Equalities and Human Rights Commission.

Metropolitan Police commissioner Cressida Dick said the former foreign secretary had not committed a criminal offence.

Asked about Mr Johnson's comments, which were made in an article for The Telegraph, she told the BBC Asian Network: "Some people have clearly found it offensive.

"I spoke last night to my very experienced officers who deal with hate crime and, although we have not yet received any allegation of such a crime, I can tell you that my preliminary view having spoken to them is that what Mr Johnson said would not reach the bar for a criminal offence. He did not commit a criminal offence."